Problem: Recently you have bought a snow walking robot and brought it home. Suppose your home is a cell (0, 0) on an infinite grid.

You also have the sequence of instructions of this robot. It is written as the string s consisting of characters 'L', 'R', 'U' and 'D'. If the robot is in the cell (x, y) right now, he can move to one of the adjacent cells (depending on the current instruction).

  * If the current instruction is 'L', then the robot can move to the left to (x - 1, y); 
  * if the current instruction is 'R', then the robot can move to the right to (x + 1, y); 
  * if the current instruction is 'U', then the robot can move to the top to (x, y + 1); 
  * if the current instruction is 'D', then the robot can move to the bottom to (x, y - 1). 



You've noticed the warning on the last page of the manual: if the robot visits some cell (except (0, 0)) twice then it breaks.

So the sequence of instructions is valid if the robot starts in the cell (0, 0), performs the given instructions, visits no cell other than (0, 0) two or more times and ends the path in the cell (0, 0). Also cell (0, 0) should be visited at most two times: at the beginning and at the end (if the path is empty then it is visited only once). For example, the following sequences of instructions are considered valid: "UD", "RL", "UUURULLDDDDLDDRRUU", and the following are considered invalid: "U" (the endpoint is not (0, 0)) and "UUDD" (the cell (0, 1) is visited twice).

The initial sequence of instructions, however, might be not valid. You don't want your robot to break so you decided to reprogram it in the following way: you will remove some (possibly, all or none) instructions from the initial sequence of instructions, then rearrange the remaining instructions as you wish and turn on your robot to move. 

Your task is to remove as few instructions from the initial sequence as possible and rearrange the remaining ones so that the sequence is valid. Report the valid sequence of the maximum length you can obtain.

Note that you can choose any order of remaining instructions (you don't need to minimize the number of swaps or any other similar metric).

You have to answer q independent test cases.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 2 ⋅ 10^4) — the number of test cases.

The next q lines contain test cases. The i-th test case is given as the string s consisting of at least 1 and no more than 10^5 characters 'L', 'R', 'U' and 'D' — the initial sequence of instructions.

It is guaranteed that the sum of |s| (where |s| is the length of s) does not exceed 10^5 over all test cases (∑ |s| ≤ 10^5).

Output

For each test case print the answer on it. In the first line print the maximum number of remaining instructions. In the second line print the valid sequence of remaining instructions t the robot has to perform. The moves are performed from left to right in the order of the printed sequence. If there are several answers, you can print any. If the answer is 0, you are allowed to print an empty line (but you can don't print it).

Example

Input


6
LRU
DURLDRUDRULRDURDDL
LRUDDLRUDRUL
LLLLRRRR
URDUR
LLL


Output


2
LR
14
RUURDDDDLLLUUR
12
ULDDDRRRUULL
2
LR
2
UD
0

Note

There are only two possible answers in the first test case: "LR" and "RL".

The picture corresponding to the second test case:

<image> Note that the direction of traverse does not matter 

Another correct answer to the third test case: "URDDLLLUURDR".

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.util.stream.Collectors;

/* el objetivo secundario no fue logrado, unicamente una de las dos funciones creadas funciona correctamente, en este caso, la funcion ordenCompatible para robotin saltarin
tuve problemas para idear la segunda parte de rehaacer la orden con los valores de <R,L,U,D>1 o <R,L,U,D>2, ademas de quedarme sin tiempo... espero que se me tenga consideracion :C, me demore 15 horas en hacer
todo este problema :_C... jelp     */


public class main {

  static class FastReader{ //https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
      BufferedReader br;   //basado en código de geeksfosgeeks
      StringTokenizer st;

      public FastReader(){
          br = new BufferedReader(new
                   InputStreamReader(System.in));
      }

      String next(){
          while (st == null || !st.hasMoreElements()){
              try{
                  st = new StringTokenizer(br.readLine());
              }
              catch (IOException  e){
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }

      int nextInt(){
          return Integer.parseInt(next());
      }

      long nextLong(){
          return Long.parseLong(next());
      }
      double nextDouble(){
          return Double.parseDouble(next());
      }
      String nextLine(){
          String str = "";
          try{
              str = br.readLine();
          }
          catch (IOException e){
              e.printStackTrace();
          }
          return str;
      }
  }


  public static void main(String arg[]) {
    FastReader lectura = new FastReader();
    int n = lectura.nextInt();
    handler selector = new handler();
    for (int i = 0; i<n; i++){
      String orden = lectura.nextLine();
      selector.select(orden);
    }
  }

}



interface robot{
    public String updateOrden ();
    public boolean ordenCompatible ();

}

class vector2 {
  private int x ;
  private int y ;
  public void vector2 (){
    this.x=0;
    this.y=0;
  }
  public void vectorModify (int x, int y){
    this.x = x;
    this.y = y;
  }
  public int[] show (){
    int [] vector = {x,y};
    return vector;
  }
}

class stringMultiply {
  private StringBuilder sb;
  public stringMultiply(){
    sb = new StringBuilder();
  }
  public void stringMultiplyy(String s, int n){
    //System.out.println(s+" :"+n);
    for(int i = 0; i < n; i++){
        sb.append(s);
    }
  }
  public String StringGenerator (){
    return sb.toString();
  }
}

class robotsimple implements robot{
  private String orden;
  private List<vector2> lista;
  private boolean cCompatible=true;
  private boolean atmost=true;

  public robotsimple (String orden){
    this.orden = orden;
    this.lista = new ArrayList <vector2>();
    this.lista.add(new vector2());
  }

  public String updateOrden (){
    //System.out.println(R+" , "+L+" : "+U+" , "+D+"  "+cCompatible);
    int R=0, L=0, U=0, D=0;
    stringMultiply ERE = new stringMultiply();
    stringMultiply ELE = new stringMultiply();
    stringMultiply UU = new stringMultiply();
    stringMultiply DE = new stringMultiply();
    char [] oIndividuales = orden.toCharArray();
    for (int i=0; i<orden.length();i++){
      if (oIndividuales[i]=='R'){
        R++;
      }
      else if (oIndividuales[i]=='L'){
        L++;
      }
      else if (oIndividuales[i]=='D'){
        D++;
      }
      else {
        U++;
      }
    }
    //
    if (cCompatible||(R!=0 && L!=0) && (D!=0 &&U!=0)){

      if (L==R){
        ELE.stringMultiplyy("L", L);
        ERE.stringMultiplyy("R", R);
      }
      if (D==U){
        DE.stringMultiplyy("D", D);
        UU.stringMultiplyy("U", U);
      }

      if (R<L){
        L=R;
        ELE.stringMultiplyy("L", L);
        ERE.stringMultiplyy("R", R);
        //System.out.println(ELE.StringGenerator());
      }
      if (D<U){
        U=D;
        UU.stringMultiplyy("U", U);
        DE.stringMultiplyy("D", D);
      }
      if (L<R){
        R=L;
        ERE.stringMultiplyy("R", R);
        ELE.stringMultiplyy("L", L);
      }
      if (U<D) {
        D=U;
        DE.stringMultiplyy("D", D);
        UU.stringMultiplyy("U", U);
      }
    }
    else {
      if (R==0 || L==0 && D!=0 &&U!=0){
        return "DU";

      }
      if (U==0 || D==0 &&R!=0&&L!=0){
        return "RL";
      }
    }
    return ELE.StringGenerator() + UU.StringGenerator()+ERE.StringGenerator()+DE.StringGenerator();
  }

  public boolean ordenCompatible (){
    int counter = 0;
    int [] compare = {0,0};
    int R=0, L=0, U=0, D=0;
    char [] oIndividuales = orden.toCharArray();
    int size = oIndividuales.length;
    for (int i=0; i<size;i++){
      vector2 vector = new vector2();
      int [] xy = lista.get(i).show();
      if (oIndividuales[i]=='R'){
        xy [0]=xy[0]+1;
        vector2 cosa = new vector2();
        cosa.vectorModify(xy[0],xy[1]);
        if (Arrays.equals(xy,compare)){
          counter++;
        }
        for (int j = 0; j<this.lista.size();j++){
          if (Arrays.equals(this.lista.get(j).show(),xy) && !Arrays.equals(compare,xy)) {
            cCompatible = false;
            return false;
          }
      }
      this.lista.add(cosa);
      R++;
      }
      else if (oIndividuales[i]=='L'){
        xy [0]=xy[0]-1;
        vector2 cosa = new vector2();
        cosa.vectorModify(xy[0],xy[1]);

        if (Arrays.equals(xy,compare)){
          counter++;
        }
        for (int j = 0; j<this.lista.size();j++){
          if (Arrays.equals(this.lista.get(j).show(),xy) && !Arrays.equals(compare,xy)) {
            cCompatible = false;
            return false;
          }
      }
        this.lista.add(cosa);
        L++;
      }
      else if (oIndividuales[i]=='U'){
        xy [1]=xy[1]+1;
        vector2 cosa = new vector2();
        cosa.vectorModify(xy[0],xy[1]);

        if (Arrays.equals(xy,compare)){
          counter++;
        }
        for (int j = 0; j<this.lista.size();j++){
          if (Arrays.equals(this.lista.get(j).show(),xy) && !Arrays.equals(compare,xy)) {
            cCompatible = false;
            return false;
          }
      }
      this.lista.add(cosa);
      U++;
      }
      else {
        xy [1]=xy[1]-1;
        vector2 cosa = new vector2();
        cosa.vectorModify(xy[0],xy[1]);
        if (Arrays.equals(xy,compare)){
          counter++;
        }
        for (int j = 0; j<this.lista.size();j++){
          if (Arrays.equals(this.lista.get(j).show(),xy) && !Arrays.equals(compare,xy)) {
            cCompatible = false;
            return false;
          }
      }
      this.lista.add(cosa);
      D++;
      }
    }
    if (R==L && U==D && counter<2){
      return true;
    }
    else{
      //System.out.println("R: "+ R + "L: "+L+"D : "+D+"U: "+U);
      return false;
    }
  }

  public void showlist (){
    for (int i = 0;i< lista.size();i++){
      int [] vector = lista.get(i).show();
      System.out.println("("+vector[0]+","+vector[1]+")");
    }
  }

  public boolean showbool (){
    return this.cCompatible;
  }
}


class robotinsaltin implements robot{
  private String orden;
  private List<vector2> lista;
  private boolean cCompatible=true;
  private boolean atmost=true;

  public robotinsaltin (String orden){
    this.orden = orden+"f";
    this.lista = new ArrayList <vector2>();
    this.lista.add(new vector2());
  }

  public String updateOrden (){
    int R=0, L=0, U=0, D=0,R1=0,R2=0,L1=0,L2=0,D1=0,D2=0,U1=0,U2=0;
    stringMultiply ERE1 = new stringMultiply();
    stringMultiply ELE1 = new stringMultiply();
    stringMultiply UU1 = new stringMultiply();
    stringMultiply DE1 = new stringMultiply();
    stringMultiply ERE2 = new stringMultiply();
    stringMultiply ELE2 = new stringMultiply();
    stringMultiply UU2 = new stringMultiply();
    stringMultiply DE2 = new stringMultiply();
    char [] oIndividuales = orden.toCharArray();
    for (int i=0; i<orden.length()-1;i++){
      if (oIndividuales[i]=='R'){
        R++;
        if (oIndividuales[i+1]=='1'){
          R1++;
        }
        else{
          R2++;
        }
      }
      else if (oIndividuales[i]=='L'){
        L++;
        if (oIndividuales[i+1]=='1'){
          L1++;
        }
        else{
          L2++;
        }
      }
      else if (oIndividuales[i]=='D'){
        D++;
        if (oIndividuales[i+1]=='1'){
          D1++;
        }
        else{
          D2++;
        }
      }
      else {
        U++;
        if (oIndividuales[i+1]=='1'){
          U1++;
        }
        else{
          U2++;
        }
      }
    }
    //
    if (cCompatible||(R!=0 && L!=0) && (D!=0 &&U!=0)){

      if (L==R){
        ELE1.stringMultiplyy("L1", L1);
        ERE1.stringMultiplyy("R1", R1);
        ELE2.stringMultiplyy("R2", L2);
        ERE2.stringMultiplyy("R2", R2);
      }
      if (D==U){
        DE1.stringMultiplyy("D1", D1);
        UU1.stringMultiplyy("U1", U1);
        DE2.stringMultiplyy("D2", D2);
        UU2.stringMultiplyy("U2", U2);
      }

      if (R<L){ //se disminuye la cantidad de L's, más pequeño es el R
        L=R;
        UU1.stringMultiplyy("U", U);
        DE1.stringMultiplyy("D", D);
      }
      if (D<U){
        U=D;
        UU1.stringMultiplyy("U", U);
        DE1.stringMultiplyy("D", D);
      }
      if (L<R){
        R=L;
        ERE1.stringMultiplyy("R", R);
        ELE1.stringMultiplyy("L", L);
      }
      if (U<D) {
        D=U;
        DE1.stringMultiplyy("D", D);
        UU1.stringMultiplyy("U", U);
      }
    }
    else {
      if (R==0 || L==0 && D!=0 &&U!=0){
        return "DU";

      }
      if (U==0 || D==0 &&R!=0&&L!=0){
        return "RL";
      }
    }
    return ELE1.StringGenerator() + UU1.StringGenerator()+ERE1.StringGenerator()+DE1.StringGenerator();
  }

  public boolean ordenCompatible (){
    int counter = 0;
    int [] compare = {0,0};
    int R=0,L=0,U=0,D=0;
    char [] oIndividuales = orden.toCharArray();
    int size = oIndividuales.length;
    for (int i=0; i<size-1;i++){
      vector2 vector = new vector2();

      int [] xy = lista.get(i/2).show();   //REMINDER, HACER UN IF PARA CUANDO SEA EL FINAL caracter "f"
      if (oIndividuales[i]=='R'){
        if (oIndividuales[i+1]=='1'){
          xy [0]=xy[0]+1;
          R++;
        }
        else if (oIndividuales[i+1]=='2'){
          xy [0]=xy[0]+2;
          R=R+2;
        }
        vector2 cosa = new vector2();
        cosa.vectorModify(xy[0],xy[1]);
        if (Arrays.equals(xy,compare)){
          counter++;
        }
        for (int j = 0; j<this.lista.size();j++){
          if (Arrays.equals(this.lista.get(j).show(),xy) && !Arrays.equals(compare,xy)) {
            cCompatible = false;
            return false;
          }
      }
      i++;
      this.lista.add(cosa);

      }
      else if (oIndividuales[i]=='L'){
        if (oIndividuales[i+1]=='1'){
          xy [0]=xy[0]-1;
          L++;
        }
        else if (oIndividuales[i+1]=='2'){
          xy [0]=xy[0]-2;
          L=L+2;
        }
        vector2 cosa = new vector2();
        cosa.vectorModify(xy[0],xy[1]);
        if (Arrays.equals(xy,compare)){
          counter++;
        }
        for (int j = 0; j<this.lista.size();j++){
          if (Arrays.equals(this.lista.get(j).show(),xy) && !Arrays.equals(compare,xy)) {
            cCompatible = false;
            return false;
          }
      }
      i++;
      this.lista.add(cosa);

      }
      else if (oIndividuales[i]=='U'){
        if (oIndividuales[i+1]=='1'){
          xy [1]=xy[1]+1;
          U++;
        }
        else if (oIndividuales[i+1]=='2'){
          xy [1]=xy[1]+2;
          U=U+2;
        }
        vector2 cosa = new vector2();
        cosa.vectorModify(xy[0],xy[1]);
        if (Arrays.equals(xy,compare)){
          counter++;
        }
        for (int j = 0; j<this.lista.size();j++){
          if (Arrays.equals(this.lista.get(j).show(),xy) && !Arrays.equals(compare,xy)) {
            cCompatible = false;
            return false;
          }
      }
      i++;
      this.lista.add(cosa);

      }
      else if (oIndividuales[i]=='D'){
        if (oIndividuales[i+1]=='1'){
          xy [1]=xy[1]-1;
          D++;
        }
        else if (oIndividuales[i+1]=='2'){
          xy [1]=xy[1]+2;
          D=D+2;
        }
        vector2 cosa = new vector2();
        cosa.vectorModify(xy[0],xy[1]);
        if (Arrays.equals(xy,compare)){
          counter++;
        }
        for (int j = 0; j<this.lista.size();j++){
          if (Arrays.equals(this.lista.get(j).show(),xy) && !Arrays.equals(compare,xy)) {
            cCompatible = false;
            return false;
          }
      }
      i++;
      this.lista.add(cosa);

      }
    }
    if (R==L && U==D && counter<2 ){
      return true;
    }
    else{
      //System.out.println("R: "+ R + "L: "+L+"D : "+D+"U: "+U);
      return false;
    }
  }

  public void showlist (){
    for (int i = 0;i< lista.size();i++){
      int [] vector = lista.get(i).show();
      System.out.println("("+vector[0]+","+vector[1]+")");
    }
  }

  public boolean showbool (){
    return this.cCompatible;
  }
}



class handler {
  //robotSimple cosa = new robotSimple(opcion);

  void select (String path){
    char [] oIndividuales = path.toCharArray();
    boolean noSaltarin = true;
    for (int i = 0; i<oIndividuales.length; i++){
      if (oIndividuales[i]=='1' || oIndividuales[i]=='2'){
        noSaltarin = false;
      }
    }
    if (noSaltarin){
      //System.out.println("no saltarin");
      robotsimple cosa = new robotsimple(path);
      if (cosa.ordenCompatible()){
      //System.out.println("orden Compatible");
        if (cosa.showbool()){
          System.out.println(path.length());
          System.out.println(path);
        }
        else {
          System.out.println(cosa.updateOrden().length());
          System.out.println(cosa.updateOrden());
        }
      }
      else {
        System.out.println(cosa.updateOrden().length());
        System.out.println(cosa.updateOrden());
      }

    }
    else if (!noSaltarin){
      System.out.println("saltarin");
      robotinsaltin cosa = new robotinsaltin(path);
      if (cosa.ordenCompatible()){
        System.out.println("orden Compatible");
        if (cosa.showbool()){
          System.out.println("camino Compatible");
        }
        else {
          System.out.println("camino no Compatible");
        }
      }
      else {
        System.out.println("orden no Compatible");
      }
    }
  }
}